Notes for the website: tendingtodivinity-theshapeofmathematics.com, (or, as you may have found, a variety of other URLs).   I'm self-taught.   In school, in the '70s, I was disinterested and didn't learn much.   Math was done largely by hand then, at that level; so I didn't gain an appreciation for the beauty of the curves, "the shape of mathematics", until later when my father gave me a computer.   This, long given away and longer of date, was an 8088 based machine with a monochrome monitor, (amber), and a Turbo C compiler.   Working in isolation, I started writing small math applications, and while the rest of the world viewed fractals and other truly advanced math, I was discovering some very basic, quaint things about parabolas.   Happily.

When I decided to add math pages to the pre-existing nolongermichael website, (now closed), I chose "The Shape of Mathematics" as their banner; as though I was proudly presenting something new, rather than just new to me.   I've become conscious of that.   I've taken up the study of what other people have found, as I offer the world what I find.   I am humbled by what has already been discovered ; and knowing this, find the things most diminished are claims to have been there first.   Still I'd have one.   I hope that what I've added to the field includes a sense of wonderment, and the desire to find more.   Beyond that...

The questions may arise: "Does he know what he's talking about?"   To this I have no simple answer.   There may be mistakes.   I hope there are not, but as I do my own fact-checking, it's possible I repeat my errors.   The shapes are what math has made them, they are not false.   If you enter the same numbers in the same functions, you should see the same result; (although there are some application display artifacts which would be difficult to duplicate, and others which I've edited out).   "Does he know where he's throwing salt?"   Again I can only answer this partially.   There was a Christian ardently opposed to the Sign of Dichotomy, and others who found in it what they already knew.   Proper women have marched Aphrodite's Curves to the trash can.   Some people like the work and others don't.   I believe it.

There are some nomenclatural errors ; (or nomenclatorial, depending on the dictionary).   This comes from making up my own terms for things, or from misunderstanding a word heard in other contexts.   Sometimes I have one to myself, saying "triabola", and meaning "cubic function".   Sometimes not.   My use of the expression, "root envelope", is definitionally awkward, as a mathematical envelope is built from tangents, and I have not demonstrated that the rootcurves included are tangents.   Although I like the expression, I am moving to use "curtain", and "flower" instead, as these are not part of mathematical language.   (The math term "surface" might also be applicable).   Another example was "mathematicism".   Surprisingly, the .com for this obscure but historically important term was available.   I felt I had made it up, so I picked it up and linked it up, before I looked it up.   My bad.   It dated back to the 17th century and René Descartes, who with his successors sought "to solve and to dissolve metaphysical problems", (Britannica Online), during the Renaissance and Enlightenment; (and beyond).   What I'm doing may be close to what they were, but I think we proceed from different motives.   I'm not trying to negate spirituality, but to bring it into a mathematical context.   Further, I doubt they would have much regard for me, for they championed mathematical rigor, while I see rigor only as the lines one must color within, and celebrate interpretation.   Math, to me, implies spirituality, and I'm quite satisfied to leave it at that; even though I think, with time, the two will meet.

I thank, but do not represent: the Schaum's Outline Series, Wikipedia.org, the MacTutor Archive, REA's Problem Solver Series, Spark Notes, and the CRC Concise Encyclopedia of Mathematics.   (If I knew everything in all these resources, I'd be as a god.)

These images were generated in Mathcad, and (recently) in Mathematica, before being transferred to Photoshop, and Illustrator.   The site was prepared in GoLive, and (recently) Dreamweaver.   I currently preview the work in Mozilla Firefox, (free to download from mozilla.com).   Site hosting is by 1&1 Internet, (naturally), and unless otherwise noted, all work is by the author, Michael Charles Young.   Thanks for visiting.